From both the technology management and economic points of view, knowing the quantity of substances processed in large and closed industrial equipment is essen­tial. In the same time, in most cases, removal of large quantities of substances for volume or mass measurement outside the equipment is not feasible, or else it would cause considerable contamination and substance loss.

For substances that are or can be stirred to a homogeneous mixture, the radio­tracer technique offers a simple method for determining their quantity. The known dosage (activity and volume) of a radiotracer should be added to the substance of unknown quantity, and after thorough mixing, a sample should be taken for
determining the radioactive concentration of the homogeneous mixture. The decrease in radioactivity compared to that of the tracer reflects the dilution rate of the tracer in the total quantity of the substance. Thus, the simple isotope dilution principle (discussed in Section 10.1.6.1) can be applied to the measurement:

Va0 1 j = (V 1 Vj)ah (11-14)

where V is the volume of the substance to be determined, Vj is the volume of the tracer, a0 is the radioactive concentration of the substance to be determined, aj is the radioactive concentration of the tracer, and ah is the radioactive concentration of the mixture developed after homogeneous stirring.

Arranged to the volume of the substance to be measured:

V = Vj (11.15)

ah — a0

As a0 = 0 and aj» ah:

V = Vj a (11.16)

ah

Consequently, the volume (V) of the substance in the equipment can be deter­mined by measuring the volume (Vj) and radioactive concentration (aj) of the tracer as well as the radioactive concentration of the pool (ah) afrer dilution. Equations

(11.11) —(11.13) are valid not only for volumes but also for masses; therefore, sub­stance masses can also be determined based on the same principle.

A well-known example of the substance quantity (mass or volume) determina­tion with the radiotracer technique is the regular measurement of metal mercury mass (used as a cathode metal) circulating in chloro-alkali-electrolysis cells. For this measurement, the Hg-203 radioisotope is used in metal mercury form with activity of 37 MBq per electrolysis cell. In one cell, approximately 1 —4 tons of mercury is circulated, and generally, 40 electrolysis cells are operated in one plant.

Some additional examples of substance quantity measurement with radiotracer technique are mentioned here:

• Determining the slag quantity in metallurgical shaft and cupola furnaces.

• Determining the metal melt quantity in electric furnaces.

• Determining the raw meal residue in fluidization homogenizers in a cement factory.